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The problem of Multi-Agent Path Finding (MAPF) calls for finding a set of conflict-free paths for a fleet of agents operating in a given environment. Arguably, the state-of-the-art approach to computing optimal solutions is Conflict-Based Search (CBS). In this work we revisit the complexity analysis of CBS to provide tighter bounds on the algorithms run-time in the worst-case. Our analysis paves the way to better pinpoint the parameters that govern (in the worst case) the algorithms computational complexity. Our analysis is based on two complementary approaches: In the first approach we bound the run-time using the size of a Multi-valued Decision Diagram (MDD) -- a layered graph which compactly contains all possible single-agent paths between two given vertices for a specific path length. In the second approach we express the running time by a novel recurrence relation which bounds the algorithms complexity. We use generating functions-based analysis in order to tightly bound the recurrence. Using these technique we provide several new upper-bounds on CBSs complexity. The results allow us to improve the existing bound on the running time of CBS for many cases. For example, on a set of common benchmarks we improve the upper-bound by a factor of at least $2^{10^{7}}$.
We discuss the connection between computational social choice (comsoc) and computational complexity. We stress the work so far on, and urge continued focus on, two less-recognized aspects of this connection. Firstly, this is very much a two-way stree
Itemset mining is one of the most studied tasks in knowledge discovery. In this paper we analyze the computational complexity of three central itemset mining problems. We prove that mining confident rules with a given item in the head is NP-hard. We
When the users in a MIMO broadcast channel experience different spatial transmit correlation matrices, a class of gains is produced that is denoted transmit correlation diversity. This idea was conceived for channels in which transmit correlation mat
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types of spin c
Participatory budgeting (PB) is a democratic process where citizens jointly decide on how to allocate public funds to indivisible projects. This paper focuses on PB processes where citizens may give additional money to projects they want to see funde